Answer:
• (a)f[g(x)]=(3x-84)/4
,
• (b)7.5
Explanation:
A function that converts shoe sizes in France to those in England is:
[tex]g(x)=\frac{3x-94}{4}[/tex]
A function that converts shoe sizes in England to those in the United States is:
[tex]f(x)=x+\frac{5}{2}[/tex]
Part A
To find a function that converts shoe sizes in France to those in the United States, we evaluate the composition, g(f(x)).
[tex]\begin{gathered} f(x)=x+\frac{5}{2} \\ f[g(x)]=g(x)+\frac{5}{2}=\frac{3x-94}{4}+\frac{5}{2}\frac{=3x-94+10}{4} \\ \implies f[g(x)]=\frac{3x-84}{4} \end{gathered}[/tex]
A function that converts shoe sizes in France to those in the U.S is:
[tex]f[g(x)]=\frac{3x-84}{4}[/tex]
Part B
Given a size 38 shoe in France:
[tex]f[g(38)]=\frac{3(38)-84}{4}=\frac{114-84}{4}=\frac{30}{4}=7.5[/tex]
A size 38 shoe in France is of size 7.5 in the United States.
